The new CBS show starring the lovely Tea Leoni as an affable, idealistic secretary of state isn’t supposed to be scary. But what if it wasn’t pure fiction? After all, even the title is stolen from a book by Madeline Albright.

“Madam Secretary” has yet to find much of an audience, or rise much beyond network-TV’s inanities and mediocre clichés (You know: Look at me, I can joggle family life and run the world at the same time.)

But it was picked up for a full season this week, and CBS entertainment-division chief Nina Tassler says it’s one of her favorite new shows.

So it may survive for a while on TV — even as policies based on the passionately-held ideals of the fictional Secretary Elisabeth McCord are imploding all over the place in real life.

The heroic McCord has a soft spot for Africa, as we learned in last week’s episode: When innocents are slaughtered after a coup in the fictional Republic of West Africa, she manages to manipulate all of Washington, including the oh-so-principled president, to get America involved — even though we have no interests there.

In true “lead from behind” fashion, we send over a couple of aging transport planes to help the good guys, and thus convince France, the African Union and the United Nations to intervene.

Here’s reality: The United States hasn’t done much to stop massacres in sub-Saharan Africa for years. We’re yet to hear even a peep about helping Burkina Faso, which is now experiencing a scenario like the fictional one seen on the show.

In the Obama years, only France has done its bit, getting involved militarily in Mali and the Central African Republic.

We’re doing nothing much to #BringBackOurGirls, and even our efforts to help against Ebola came too late — new cases in West Africa peaked weeks ago. (Kudos, though, to UN Ambassador Samantha Power for this week’s courageous but largely symbolic trip there.)

In another “Madam Secretary” episode, McCord tussles with Canada’s ambassador to Washington over a fictional pipeline.

Salvation comes only when the secretary manages to bury her own department’s study, which suspiciously concluded that the pipeline isn’t harmful to the environment. That study, we discover, is badly tainted because it was sponsored by evil oil corporations. Evil Canada shuts up.

Minus the manipulating oilmen, that plot did resemble reality: After studying Canada’s Keystone XL to death, the State Department concluded in January that the pipeline’s effect over greenhouse gases is negligent. Yet President Obama still won’t approve the project — pending further studies, of course.

Then there’s the show’s big multi-episode story arc: McCord must salvage diplomatic talks with Iran, which are being undermined by countless Washington war mongers.

See, the president recruited our heroine, a former CIA operative and an academic, after her predecessor got killed in mysterious circumstances.

As the show progresses, we learn that even within the administration some powerful officials oppose the president’s attempt to make nice to the Iranians — and that may have to do with the former secretary’s death.

Manipulated by lowlives such as a Las Vegas casino mogul, these greedy enemies of peaceful solutions stop at nothing. But our idealistic-yet-tough heroine manages to advance diplomacy just a bit on each episode, fending off her powerful DC foes.

Back in reality, many in Washington, including a growing chorus of bipartisan skeptics in Congress, do indeed fear that President Obama’s talks with Iran will leave this long-time US enemy too close to possessing nuclear weapons.

And true: Just as green billionaires finance the anti-Keystone campaign, Vegas mogul Sheldon Adelson donates to the cause of stopping Iran from obtaining a bomb.

“Madam Secretary” has one noteworthy good guy besides McCord: the hunky Iranian UN ambassador, Zahed Javani. When she was at CIA, McCord had close ties with him, so much so that her colleagues called him her “boyfriend.”

Who cares, — it’s only Hollywood, right?

But what if it turns out that our policy-makers see the world just as the “Madam Secretary” writers do? What if they really believe that all world crises can be resolved in a neat, morally correct package? What if our leaders really have concluded that we need to beat up on America’s allies (Canada) and turn our enemies (Iran) into a boyfriend?

More and more Americans find that possibility not only scary, but all too believable.